Cloth? It doesn't have to be special, per-say... Just something that isn't too absorbant, dry, and also that doesn't leave much lint behind. Usually you can buy painter's rags at stores in bunches. They are lint free, and not treated with chemicals like any soaps or detergents which could just mess with the paint or rags themselves. Also, it's best if you wait for the paints to fully dry... I mean FULLY dry before black washing. Since, when painting, the solvents in the wet paint start to reactivate the dry paint, making it tacky, and able to smear. Try not to rub too hard, or too much. Spray just enough so you only have to make about 2, or 3 wipes in mostly the same direction. After all, black washing is really only meant to fill in scratches, and recessed areas, and to slightly darken your color. If your afraid to try something on your finished product, ALWAYS test your technique on something else with very similar characteristics. And follow the same steps, and try to mimic the same conditions... Temperature, humidity, direct sun, same room or environment, if using a heat gun... Anything. Also, what material your painting makes a difference also. The hardness, and texture.
Most people make the mistake of not really giving the paints enough time to flash off, and dry. They think that as soon as it's dry to the touch, they can do whatever, when it's just the surface that's dry, and the paint is still flashing underneath, by evaporating through. Adam, and some of these other guy's are in a very hot, dry area, so spray painting is quick, and they have an advantage. Even Adam said, make sure they are really dry.
To be on the really safe side, I let a day pass before coats.